Question

What is the slope of any line perpendicular to the line passing through `(4,2)` and `(-1,10)`?

Answer 1

`5/8`

Explanation:

First figure out the slope of the line that passes through those points using the slope formula:

`(y_2-y_1)/(x_2-x_1)` where `y_2=10, y_1=2 and x_2=-1, x_1=4`

So:

`(10-2)/(-1-4)=8/-5=`slope

NOTE: You could also let `y_2=2, y_1-10 and x_2=4, x_1=-1`
Which leads to the same answer (thanks Tony B.!):

`(2-10)/(4-(-1))=(-8)/5=`slope

Perpendicular lines always have different signed slopes (meaning if one line's slope is positive, the perpendicular line's slope is negative and similarly negative `->` positive). Thus our slope is positive.

Also perpendicular lines are reciprocals of each other so our new slope is:

`5/8`